More specifically, the purpose of the workshop was to address the following two central questions: (i) how are the two forms of reasoning different (if indeed they can be distinguished) and (ii) how can they be integrated together in an Artificial Intelligence enviroment? The workshop was therefore structured around two panel discussions, one on each of these central issues, together with an invited talk for each session. In each of the panel discussions four of the submitted papers were briefly presented by their authors raising problems and questions for the subsequent discussion.
The workshop started with the presentation of the results of an on-line questionnaire which was filled out before arriving at the workshop, as these results provided some insight into the main points of agreement and controversy. The majority of respondents agreed on a definition of induction as inference of general rules from specific observations. Another viewpoint that seemed uncontroversial is that abduction and induction are reasoning forms stemming from a common root. The proper definition of abduction, and its relation with induction, appeared to be more problematic. Roughly two-thirds of the respondents agreed with the definition of abduction as inference to the best explanation, while one-third favours a definition of abduction as hypothesis formation. The main features that distinguish between abduction and induction mentioned by the respondents are: the form of the inferred hypotheses, the utility of the inferred hypotheses, the underlying consequence relations, and the computational methods employed.
2. Peirce on abduction and induction
It was also felt useful to have at the beginning of the workshop a
short presentation of abduction and induction as introduced and
studied by the American philosopher Charles Sanders Peirce.
Consider the Aristotelian syllogism Barbara:
Whereas Peirce's classification of reasoning forms through syllogisms is probably well-known in Artificial Intelligence, it appears to be much less known that Peirce abandoned his syllogistic theory around 1900 in favour of a classification of reasoning forms in terms of the function they perform in science. Three stages are discerned: (1) formulating a hypothesis, (2) drawing predictions from the hypothesis, (3) evaluating these predictions.
The first stage, coming up with an explanatory hypothesis, is what Peirce now calls abduction. Predictions are drawn by deduction; and assessing a hypothesis by evaluating these predictions in the real world is what Peirce calls induction. The whole process is triggered by some surprising observation, and Peirce formulates the following requirement for a hypothesis to be explanatory:
It should be noted that Peirce's later definition of abduction covers both the second and third syllogism quoted from his early theory, since in both syllogisms the inferred hypothesis entails one of the premisses given the other. One could say that in his later theory Peirce concentrates on the inferential characteristics of abduction (a sort of reversed deduction), while in his early theory he emphasises syllogistic (i.e. syntactical) characteristics.
Some of the workshop participants adhere to the inferential perspective, and therefore view induction as a special case of abduction, while others favour the syllogistic perspective, and therefore stress the differences between abduction and induction. These points formed a central part of the discussion in the panels that followed.
3. Invited talk: John Josephson
The second invited speaker Ryszard Michalski
unfortunately was not able to attend the workshop
In his invited talk, John Josephson (Ohio State University) defined abduction as inference to the best explanation or explanatory inference, following a pattern like this:
As for the relation between abduction and induction, it was argued that inductive generalisation is a special case of abduction. The explanation occurs on a metalevel: while the generalisation "all crows are black" does not explain why a particular crow is black, it does explain why we observe a black thing whenever we observe a crow. Furthermore, in induction we are not just interested in any generalisation, but only in the best one(s) (an amusing example of a bad inductive argument is "This thumb is mine; that thumb is mine; therefore, all thumbs are mine").
We thus see that Josephson's position corresponds more or less to Peirce's later theory of abduction as hypothesis formation, but extending it to include hypothesis selection as well.
The slides Josephson used for his presentation can be found at http://www.cis.ohio-state.edu:80/~jj/abduct_induct.ps.
4. Discussion panel 1: Distinguishing abduction and
induction: are they different and how?
Atocha Aliseda (Stanford University, USA) argued that abduction and
induction are best perceived as two points in a whole spectrum of
explanatory reasoning. Different forms of explanatory reasoning can
be obtained by instantiating three parameters: the kind of
inference involved in explaining, the kind of observation that
needs to be explained, and the kind of explanations (facts, rules
Brigitte Bessant (Universite d'Artois, France) pointed out that we can only increase our insight in abduction and induction if we reach a better understanding of the fundamental concepts on which these reasoning forms are based. Among these fundamental concepts are: the notion of generality between inductive hypotheses, the notion of explanation, and the notion of confirmation (what does it mean for an observation to confirm a hypothesis?).
Marc Denecker (Katholieke Universiteit Leuven, Belgium) argued that syntactical distinctions between abductive hypotheses as ground facts and inductive hypotheses as theories are unsatisfactory. Instead, he proposed a semantic characterisation of the difference between the two by means of possible world models characterisation exploiting a more abstract distinction between general and specific knowledge.
Erich Prem (Austrian Research Institute for AI, Vienna) provided an analysis of the three forms of reasoning from the classical Aristotelian viewpoint, stressing that logic is not so much a "science of truth" or a "science of reasoning", but rather a science of argumentation.
5. Discussion panel 2: Synthesis of abduction and
induction: can they be put thogether and how?
John Bell (QMW, University of London, UK) suggested that induction and
abduction are both forms of pragmatic, or context-dependent,
reasoning. Given a partial epistemic context, induction is
the process of expanding the context in the appropriate way and
then reasoning deductively, while abduction is the
process of expanding the context in the appropriate way
such that a purported conclusion can be deduced from it.
The notion of pragmatic entailment can be
used to provide a common model-theoretic framework for
induction and abduction.
Nicolas Lachiche (INRIA, France) presented a formal separation of abduction and induction by relating each one to a different form of completion of the given background knowledge base. This distinction though is confined only to the specific case of confirmatory induction.
Stathis Psillos (London School of Economics, UK) proposed a set of desiderata that a general model of ampliative reasoning from incomplete information should satisfy. As Josephson, Psillos argued that abduction understood as inference to the best explanation best satisfies these desiderata, encompassing inductive generalization as a special case.
Fabrizio Riguzzi (Universita di Bologna, Italy) presented a framework in which it is possible to integrate abduction and induction as these are used in the context of Logic Programming. This can increase the learning capabilities of Inductive Logic Programming, as it allows a system to learn abductive logic programs from background programs with integrity constraints.
6. Summary of discussions
It was clear from the beginning that there would be many different
opinions on the issues addressed among the participants.
Furthermore, it transpired that it was not easy to agree, at the
current stage of the debate, on the list of the particular problems
and issues that should form the central points of investigation in
the overall task of analysing the relation between abduction and
induction. Two main schools of thought emerged. In the first the
emphasis is put on unifying the two into a common form (identifying
one as a special case of the other) while in the second the
emphasis is on clearly separating the two by identifying their main
characteristics. Hence the need to have two conceptually different
forms of ampliative reasoning from incomplete information was put
On the other hand, if two such forms should exist we need to clarify the differences in their operation and also the difference in the tasks that they can achieve. One difference that most people seemed to agree upon is that abduction presupposes a general theory about the domain of interest. The abductive explanations or conclusions are understood relative to this theory. Furthermore, it emerged that the utility for each form (and the subsequent computational model) may be an important distinguishing indicator of the two. While it was argued that the two can be conceptually unified under abduction (itself interpreted as inference to the best explanation) using a meta-theory of sampling as the "causal" theory for induction, it was pointed out that problems in AI seem to need two quite distinct forms of reasoning for different tasks employing different computational models.
In this AI (perhaps extreme) view we should not expect that there are Platonic ideals of abduction and induction that we are trying to capture but rather that abduction and induction are simply processes that are needed for solving practical problems. However, the discussions at this workshop seemed to suggest that many people do try to capture Platonic ideals, but that these ideals differ among different people. In particular, some of the work presented in the workshop has provided a possible first step towards such a Platonic separation of the two using possible world semantics to formalise their differences. If indeed there are many such alternative proposals, then the first and perhaps most important step is to disentangle these different ideals, and to distinguish them terminologically. Only then can we hope to formalise them in a satisfying manner.
7. Concluding remarks
Perhaps the main result of this workshop was to bring to the
fore, and make people aware of, the different perspectives on
abduction and induction. The continued discussions between the
participants on the days that followed, well after the workshop had
ended, indicate the useful role that it has played in putting
together these ideas. We feel that we are now in a better position
to formulate the main issues that need to be addressed before we
can develop a coherent account of abduction and induction.
The short time available did not allow ample discussion around the
second central question of "how can abduction and induction be
integrated together in an Artificial Intelligence environment" which in
fact was overshadowed by the first issue of the comparison and
distinction of the two forms of reasoning. This issue of integration
will be taken up at a follow-up workshop.
In the meantime, an electronic mailing list has been established for continuation of the discussions started at the workshop. Those interested in participating in this mailing list should send an email to Peter.Flach@kub.nl.
The workshop notes contain 15 short papers and are available on-line through the workshop's WWW-pages at http://machtig.kub.nl:2080/ECAI96/; a limited number of hardcopies is still available from Marc Denecker (email: Marc.Denecker@cs.kuleuven.ac.be).
This workshop has been made possible by financial support from the European Networks of Excellence CompulogNet (Computational Logic) and MLnet (Machine Learning). Writing of this report has been partially supported by the Esprit Long Term Research Project 20237 (Inductive Logic Programming 2).